^'^^^ ANSWERS TO PROBLEMS 

HANCOCK'S APPLIED MECHANICS 
FOR ENGINEERS 



REVISED AND REWRITTEN 



BY 



N. C. RIGGS 

PROFESSOR OF THEORETICAL AND APPLIED MECHANICS IN THE 

SCHOOL OF APPLIED SCIENCE OF THE CARNEGIE 

INSTITUTE OF TECHNOLOGY 



THE MACMILLAN COMPANY 
1916 

All rights re/nerved 



ANSWERS TO PROBLEMS 

HANCOCK'S APPLIED MECHANICS 

FOR ENGINEERS 



REVISED AND REWRITTEN 



BY / 

Nf C:" RIGGS 

I 

PROFESSOR OF THEORETICAL AND APPLIED MECHANICS IN THE 

SCHOOL OF APPLIED SCIENCE OF THE CARNEGIE 

INSTITUTE OF TECHNOLOGY 



THE MACMILLAN COMPANY 
1916 

All rights reserved 



V • 






N\ 



If 16 



Copyright, 1916, 
By the mac mill an COMPANY, 



Set up and electrotyped. Published November, 1916. 



f^!- 



r 



NoriDoott ^ress 

J. 8. Cashing Co. — Berwick & Smith Co. 

Norwood, Mass., U.S.A. 

©CI.A445575 
NOV -9 1916 






ANSWERS. 



1. 154 lb., E. 19" N. 2. 119 lb., 68.9° above hor., proj. S. 1.8° E. 

3. 86.60 lb., 150° with x-axis. 4. i^= 106.6 lb., iV= 188.6 lb. 

5. 14.14 tons tens, in J., 19.32 tons compr. in B. 

6. 418.8 lb., 234.5 lb. 7. 2833 lb. at A, 4167 lb. in BG. 

8. 209.8 lb. tens, in ED, 542.2 lb, at foot. 

9. 4 tons at A, 3.464 tons in BC. 10. 1000 lb., 748 lb., 523 lb. 

11. Tens., 726 lb., 512 lb., 279 lb. ; reaction, 774 lb., 930 lb., 1024 lb. 

12. 2263 1b. 13. 14.14 lb. at each point. 15. 259.8 1b. 

16. If angles 7 are acute, B = 110 lb., direction angles are 98° 10', 
89° 33', 8° 11'. 

17, Back-stay 16.68 tons, each leg 16.74 tons. 

■ 18. (1) 120 lb. 4 in. from 100 lb. force. (2) 80 lb. 6 in. from 100 lb. 
force. 

19. .8 P, .2 P. 20. End of pilot 8 ft. 11.5 in. from end of turn-table. 

21. 1.54 ft. from AB, 1.28 ft. from BC. 23. 5.59 ft. from 0. 

25. B = 175, center (3.57, 1.14, 3.74). 

27. Three fourths of the distance from any vertex to the intersections 
of the medians of the opposite face. 

29. 2.5 ft. from PiPo, .833 ft. from P1P4. 

31. .726 in. from bottom. 32. 2.32 in. from bottom. 

33. 3.70 in. from bottom. 34. c. g. is distant K^^ + ^ai) ^^^^ ^^^ 

3(^2 + «i) 
35. 2.94 in. from bottom. 36. 5.91 in. from bottom. 

37. .375 in. from center of disk. 

38. (5.951, 6.095, 6.095) when 2 in. -cube is removed from corner at 
origin and 3-in. cube from other corner on a;-axis. 

43. (.3 a, .75^). 44. .223 P from straight edge of remaining area. 

45. a; is decreased .0063 in. 55. 4.61 in. from closed end. 

56. 5.36 in. from closed end. 
57 6 H^R^ - r2) -H 8 ^(P3 - r3) + 3(P^ - r^) _ 
12 H{R^ - r2) -f 8(P3 - 1^) 

1 



ANSWERS 



58. 5. in. 59. 5 in. 60. 2.256 ft. from center. 

61. 2.86 from ?/-axis. 62. 2.36 from a--axis. 

63. 7.18 ft. from 1200 lb. weight. 64. .60 radius from center. 

65. .90 radius from center. 68- f length of axis from vertex. 

70. 35,833 cu. ft., 10.7 ft. from surface by Simpson's formula, 35,750 
cu. ft., 10.8 ft. from surface by second formula. 

72. 15.24 sq. in., 2.96 in. from the base. 73. 4.8-3 in. from bottom. 



74. 

79. 
82. 



7rr^ 



75. 



4r 



2 TT^a^r. 



■wh 
6« 



om center. 


76. 


lirf^h. 78. -ah'^ 

'2 

2r ^ 


80. 4 7rr2. 




81. from center 



'-iiii^ + ^d^y -h^]. 



83. 20 lb. at parallel to original force, and couple of forces of 50 lb. 
each. 

84. M^=- 500 lb. -in., 3Iy = - 642.8 lb. -in., 31, = - 580.4 lb. -in. 

85. M = 233.2 Ib.-in., angles 59° 2', 120° 58', 133° 19'. 

86. B = 26.93 lb., angles 56° 9', 42° 2', 68° 12'. 
308.1 Ib.-in., 49° 31', 60° 52', 54° 15'. 

87. 252.98 Ib.-in., 18° 26', 90°, 108°26'. 

88. 40.31 Ib.-ft., 51° 40', 41° 54', 104° 22'. 

91. 435 lb. at origin, inclined 312° 50' to horizontal, and a couple of 
moment 3350 Ib.-ft. 

92. AB 5000 lb., BC 707 lb., CD 0304 lb., CE 4500 lb. 

93. r = 8081 lb.. Pi = 2000 lb., P2 = 10,000 lb., P3 = 14,142 lb., 
Hh = 5714 lb., Ff, = 13,714 lb. 

94. T = 4368 lb., C = 11,263 lb., T' = 0364 lb. 



95. Hor. comp. 



tan a + tan /3 



On right-hand member, upper 



end, vert, comp., up, ^ (Tr+ 6^ + j (^Q tan oc -f 1 (j^tan ^^ ^^^^^ ^^^^ 

tan a -\- tan /3 



(W+l G>) tan cc - I (^ tan /3 

r=3730, O, X=7010, 



vert, comp., down, = 

tan a -{- tan j3 

96. At A 1370 lb. vertical; P, X= 7010, 
Y= 6960, E, X= 7010, F = 7060. 

97. AB .943 tons, BC .75 tons, DC .118 tons, Z)P.583 tons, EC .667 
tons. 

98. T = 3.50 tons, r= 1.90 tons, at A 5.76 tons, at B 6.63 tons. 

99. CD 1.413 tons, BC 10.455 tons, BE 21.16 tons. Reaction 
at B 33.42 tons, reaction at A 34.43 tons, EG 21.54 tons, EE 7.84 
tons. 



ANSWERS 3 

100. BC 11.71 tons, BF 39.36 tons, EF 14.58 tons, pin force at inter- 
section of AB and BC 2.07 tons, reaction at A 61.37 tons. 

101. Tens. = 14.85 tons, pin reaction = 20.64 tons. 

102. ^C 707 lb., CE 5000 lb. 

104. P = 62.5 lb., X'z= 222.5 lb., Y' = 76.39 lb. X" =. 52.5 lb., 
r" = - 13.89 lb., Z" = 130 lb. 

105. ( r-axis parallel to P) P=62.5 lb., X' = 191.79 lb., r' = -38.19 lb., 
X" = 46.36 lb., Y" = - 36.81 lb., Z" = 130 lb. 

106. (a) Boom, 30 tons, at A 7.28 tons at 1°38' with boom, at B 
12.43 tons at 46°38' with mast, tens in each leg 30 tons. (6) In legs 
36.74 tons and 21.21 tons. If boom weighs 4000 lb., tension in each leg 
31.65 tons. 

107. Using values from Problem 104, with crank-pin below shaft, and 
assuming line of G' to be 6 in, from x-axis ; P = 62.5 lb,, X' = 131.1 lb., 
X' = 13.9 lb., r = 76,39 lb., T" =:- 13.89 lb. 

108. 4566 lb. at 79 '47' with BA, 5.24 ft. from A. 

109. P4 = 2 tons, P5 = 2.5 tons. 110. P 780 lb., ^ 1065 lb. 

111. Left 2.71 tons, right 2.12 tons. 

112. Left 2.65 tons, right 2.30 tons. 

113. Left half, upper chord, .676, .538; lower chord ,563, .375; web 
members .208, .188. 

114. Reactions, left .639, right .361 ; stresses, upper chord from left 
.583, .583, .541, .541, lower chord .701, .250, .250, web members .5, 
.451, 0, 0. 

115. Taking vertical load as unity ; upper chord from left .968, .830, 
.809, .947 ; lower chord .914, .500, .688 ; web members .458, .414, 
.188, .208. 

116. Upper chord from left (in tons) 4.91, 4.91, 7.51, 5.48, 5.48, lower 
chord 2.45, 6.21, 6.50, 2,74, web members 4.91, 2.60, 2.60, 2.02, 5.48. 

117. Upper members from apex (in tons) 1.73, 1.73, 3.46, 5.20; lower 
members 2, 4, 6 ; web members 2, 2, 3, 2.66, 3. 

118. Left half, upper chord 8.51, 6.90; lower chord 6.10, 6.26; web 
members, 1.50, .547. 

119. Upper chord .875, .813, .750, .688; lower chord .758, .650, .433; 
web members .108, .108, .217, .108, .108, .217 (LE), .325 (XE). 

122. -bJiK 123. ^(b'^ + h-2). 
4 36^ ^ 

124, I,, = 15.44, /,, = 42.12. 125. J,, = 4.279, /,, = 79.66. 

126. 4.972, 2,772; 73.15, 17.95. 127. 20232. 128. 18785. 

129. 35694. 130. 47807. 131. I^^ = 1863, 7„^ = 1311. 



4 ANSWERS 

132. Igx = 3405o, lyy = 18853 if distance between inner vertical plates 
is 9.25 in. 

135. 205 ; 71 approx. 136. 42.24, 42.56, 42.67. 

137. Formula gives exact values. 138. 207. 139. 203.63. 

142. 1725, 90°. 

143. Semi-axes of ellipse parallel to sides, b, h, of rectangle and equal 

, . 2V3 -, 2\/3 .. 1 .,, 2V3 , V3 ,. , 

(a) and respectively, (&) - — - and ■ — respectively. 

h b h b 

144. 2464.3 and 255.7 ; axes inclined 27°17.5' to sides of rectangle. 

145. i:^ and — . 158. 5.558. 159. 595 (lb. and ft. units). 

4 4 

163. 6 r^x^ + (3 r- + h^)(if + .?-) = 12 (a:-axis along axis of cylinder). 

164. 2 r2(x2 + ?/2 + ^2) = 5. 169. 2866. 170. (a) 37.9, (&) 333. 
171. 439. 172. 2815. 173. 102, 486. 

174. C is 14.26 ft. horizontally and 9-.68 ft. vertically from A. 

175. C is 24.79 ft. horizontally and 16.83 ft. vertically from A. 

176. 57.73 lb., 28.87 lb., 57.73 lb. 

177. BC= 10.78 ft., CD = 14.35 ft., tens, in 5(7 = 44.40 lb., tens, in 
CD = 108.4 lb. 

178. Lengths 7.137 ft., 4.759 ft., 3.643 ft., 10.236 ft. ; tensions 
53.53 lb., 35.69 lb., 36.43 lb., 76.77 lb. 

180. Tensions 343, 294, 337, 481. 11=275. 181. 10.33 ft., 223.6 lb. 

190. 0, 810, 1620, 2430, 2740, lb. -ft. etc. 

191. 0, 1567, 3013, 3340, 3147, 2033, Ib.-ft. 199. 500 lb. each. 
200. 1.5 to 1. 201. 1 to 2. 202. 7933 1b. 203. 71.43,88.33 1b. 

204. Tens, at B in each cable 1616 tons, cross section of each cable 
43.1 sq.-in. 

205. 1231.27 ft. 

206. Lowest point of chord 42.7 ft. horizontally from lower support, 
H = 18240 lb., Max. tens. = 33960 lb. 

207. 127.0 ft. 208. 13.99 ft. 

209. Jr= 1000 lb., S = 200.83 ft., max. tens. =1001.2 lb. 

210. d = 5.0042 ft., length = 200.33 ft. 

211. 5000 lb., 200.004 ft. 212. 502.5 lb. 

213. 27.308 ft. from A, f? = 1.869 ft., .9=123.44 ft., max. tens.=55.1 
lb. 

214. 4.55 ft. from A (outside), d = .05 ft., S= 125.8 ft., max. tens. 
= 59.07. 

215. (1) a = 120, (2) a = 128.93. 216. (1) « = 1200, (2) a = 1201. 
217. 64 f/s, 50.6 f/s. 218. v=-kcsinct. 219. accel. = 32 f/s''^. 



ANSWERS 5 

220. The ordinate of the velocity -time curve is equal to the slope of 
the space-time curve. 

221. a = - kc-2 cos ct. 223. 1.73 sec, 85.7 f/s. 224. 580 ft., 193 f/s. 
225. 113.5 f/s, 3.52 sec. 226. 60.97 ft. 227. 0.10 ft. 

228. (3.10 ft. 234. 6.67 lb., 10.73 f/s2. 

229. 2.58 ft., .215 sec. 235. 4.65 ft. 

230. 89.7 ft. 236. 1000 lb. 

231. 11.79 f/s2, 37.68 ft. 237. 3000 1b. 

232. 10.02 ft. 238. (a) 133.3 lb., (b) 400 lb. 

233. Boy thrown forward. 239. 18.97 f/s^, 11.79 lb. 

240. 3006 ft. 241. .227 sec, 2.25 f/s, .235 in. from 0. 

242. 4.48 in. 244. 128,000 lb. per inch. 

243. 2.93 in. 245. .0229 sec, 25.37 f/s. 
246. 49.7 ft. Would not stop. Limiting distance = 62.1 ft. 

249. 23 f/s. 250. • ( 1 — e w ] 

251. lOOmi./hr. 252. 65.9 f/s. 

253. 131° 25' with direction of stream ; .378 mi. ; 5.87 min. 

254. 42.50 mi./hr., from N. 41° 44' W. 

255. (a) 66° 40', (&) 48° 52' ; 4° 20', 17° 40'. 

256. Depends on location and direction of telescope. If telescope is 
in meridian plane at equator, true direction is .32" west of apparent 
direction. (This assumes the center of the earth to be at rest. The 
motion of the earth in its orbit causes a much greater aberration.) 

257. 40 mi./hr. forward ; 40 mi./hr. backward relative to frame. 

261. at = 16.1 f/s2, an = 20 f/s^, a = 25.67 f/s^, 68° 52' with vertical, 
r=2.97 lb. 

262. Tens, in short rod = 11.55 lb. On long rod X at upper end = 
7.698 lb., Xat lower end = 13.473 lb., no. rev. per minute = 72.2. 

263. 1155 lb. 266. .8 in., 3.2 in., 7.2 in. 
267. 3.2 in.^2.8 in., 28.8 in. 

269. V = VgB, V2 gR, etc ; a = 50.8 f/s2, 72 f/s2 etc Force = I G, 
2 G, etc. 

270. VKgB 275. 23.39 tons. 

271. 2Vp. 276. 19° 23'. 

272. |. 273. 1. 277. 9.83 f/s, 21.98 f/s. 

278. .9608 sec. as compared to .9589 sec. 

279. 1.140 sec. , gf]i2 

280. 1:1.0028. jg 286. d tan«-^^^^^^. 

282. 1.64 lb. \e* 287. 131 f/s. 



6 ANSWERS 

288. 6615 ft., 9396 ft. 292. (a) 16.05 f/s, (c) 5.80 ft. 

291. (a) 16.05 f/s, (c) 12.65 ft. 293. (a) 4.34 f/s, (c) 2.42 ft. 

294. A circle of radius 124,523 ft. (neglecting air resistance). 

295. 28.47 mi. 

296. 24,470 ft. (Helie), 31,060 ft. by parabola formula. 

297. (a) 13^ 55.3', (b) 12^ 36.4'. 

298. 7.25 f/s, 9.73 f/s. 

301. .0873 rad/sec.2, 100 rev. 

302. I rad/sec.-, 11.95 rev., | rad/sec. at end of 10 sec. 

304. Max. ang, accel. = 8 tt^, rad/sec.-, max. ang. vel. = 2 tt- rad/sec. 

305. 15 f/s, 5 f/s2. 

306. Given a = k/d, d = di and w = wi when t — 0, then 



t = i Vce-' -2kd-^ vcd{^ _ 2 A;^i - A log Cd-k- vc-'e-'-2_Cke ^ 

C C ^i Cdi-k-VC-^di-^-2Ckdi 

where " C' = a;r+ — •. 

307. A helix. 

308. F„ = 0, Vb = 20 f/s, F, = 14.14 f/s at 45^ V^ = 17.32 f/s at 30% 
T"a(rel. ^) =- 20 f/s, F,(rel. A) = 14.14 f/s at 45'^, Frf(rel. E) = 5.196 
f/s at - 15^. 

310. Each 33.33 f/s- directed toward center. 

311. A 33.33 f/s2, 5 33.57 f/s-^, i> 35.19 f/s-^, E 35.39 f/s-2. 

313. (a) at = 0, «„ = 2581 f/s-, (&) max a, = — .49 f/s"^, max «„ = — 
645.57 f/s2, (c) max a« = .294 f/s2, max a„ = 645.48 f/s^. 

316. Inst. cent. 2.196 ft. below A, F^ = 7.32 f/s, ang. vel. = 1.22 
rad/sec, F^ = 9.27 f/s. Fa = 2.68 f/s. 

318. 150 r. p. m. about an axis in the plane of the two axes making 
an angle of 36° 52' with axis of shaft. 

319. TT rad/sec. about a line parallel to AB, distant 18 in. from AB 
and 24 in. from CD. 

322. 47° 58.5'. 

323. 1207.4 ft.-lb. by P, 250 ft.-lb. against R, 500 ft.-lb. against W. 
38.38 f/s. 

324. .385 ft., 141.9 ft.-lb. 328. 3006 ft. 

325. 3^5, 140 ft.-lb. 329. 2277 lb. 

330. 587,880 ft.-lb./sec, or 1069 H. P. 

331. 103 f/s, 2,784,375,000 ft.-lb., 5,062,500 H. P., 0,627,200 H. P. 

332. 195.1 ft. 333. The body would not stop. 



ANSWERS 7 

337. 6.55 in. 341. .6 in, .72 in. 

338. 18,500 lb. per inch. 342. 263 cars, 63,000 lb. per inch. 

339. 88.2 lb. 343. 376 ft. 

340. 1.79 in. 

345. 960 tons (Molesworth), 107 tons (Wellington). 

346. 55 tons (Wellington, safety factor 4). 

347. 18,212 ft.-lb., 42.6 f/s, 437 tons. 

348. 9310 lb. 350. 1.03 in., 11.6 f s. 

349. 20,794 ft.-lb. 45.6 ft. 351. 987,300 lb. 

352. 914,400 lb. 

353. 3 f/s, 2 f/s, 54 f/s, 36 f/s, 39.4 sec. 

355. 142.5. 356. 73.8 1b. 

357. 139.6 rev.; 71.8 1b. 

358. Max tens. = 100 + a/10,000 _j_ il^li^^ ^ where I = length of cord 

• j; ^ -171 ^.• max. tens. . . , 

in leet : Elongation = ■ m. per inch. 

5000 

359. 235.7 lb., 6890 lb. 364. Disk. 

360. 44.7 lb., 2306 lb. 366. 18.16 f/s. 

361. 904 1b., .249. 368. 15,860 lb., about 40 tons. 
ilOj^^ 369. 22,590 1b. 

370. 3100 tons. 
363. Sphere, disk, hoop. 371. 60 tons. 

372. (a) 87.9 lb., 33.8 lb. ; (b) 67.3 lb., 32.7 lb. ; (c) 76.4 lb., 42.7 lb. 
378. 549 1b. 379. .142. 380. .85. 

381. 2.35 H.P., 79° 11'. 383. 164, 1.96 ft.-lb. 

382. 54.3 lb. 89 lb., 83.2 lb. 385. 16.2 tons. 

386. 33.3. 387. 4-338. 388. 70.2 1b. 

389. 83.54 lb. per inch of width. 390. 47 tons. 

393. 6.6 in. 396. 717 lb. 401. 17.3. 

394. 7.49. 399. 5850 ft.-lb. 402. 100.5. 

395. 18.65, F=90f/s. 400. 6.78,15.97. 

403. ri=2087 lb., 72 = 594 lb., P = 272 lb. {Ti is assumed hori- 
zontal.) 

404. Neglecting change in K. E. of drum, P = 303 lb., Ti = 2331 lb., 
r2 = 664 1b., r= 2233 lb. 

405. 342 lb., 2630 lb., 748 lb., 2518 lb. 

406. 5. 408. 707 ft. 410. 25,050 lb. 

407. 668 ft. 409. 818 ft. 411. 509 ft. 
412. P, = 243 lb., P^ = P'^ = 0, Py = 1.11 lb., P'y = 8.89 lb 



362. \jl^ 



8 . ANSWERS 

413. P^ = 84.73 lb., P'^ =-85.26 lb., Py = 1.59 lb., P'y = 9.13 lb., 
P, = 117.8 1b. 

414. P^ =- 7926 lb., P'^ =-3963 lb., Py = 2.17 lb., P'y = 9.42 lb., 
P, = 8.73 lb. 

415. P^ = 747.5 lb., P'^ =- 747.5 lb., Py = P'y = 0, P, = 440 lb. 

416. (Assume pos. a:"-axis in direction of D from shaft in Fig. 259, pos. 
?/-axis upward, spheres of cast iron, rotation from x to ?/, and no other 
forces acting, r. p. m. being 150 when in position shown in Fig.) Then 
for (a), a=- 4.645 rad/sec.'^, at A P^ =- 172 lb., Py =-946 lb. ; at 
B P'_, = - 374 lb., P'^ = -437 lb. 

For case (6) a = 4.645 rad/sec2., a;2 _ 296.3, P^ = 249 lb., Py = 1308 lb., 
P'^ = 470 1b., P', = 6711b. 

417. Ang. accel. = .3.348, rad/sec.2, T= 49.91 lb., s = .698 ft. 

418. (a) P^ =- 592 lb., Py = 69 lb.; (b) P^=- 684 lb., Py = 0. 

419. Yel. of (5^1 = 1.76 f/s, vel. of ^^2=1.32 f/s, ang. vel. = 132 
rad/sec. 

420. .866 sec, 2.44 ft. 422. .463 sec, .7 ft. 

424. Show that (neglecting holes) /„ = 511 and that the time of vibra- 
tion should be 1.45 sec. instead of 1.3 sec 

425. 39.480. 427. 28.0 sec 429. 56.761b. 

426. 3.754 ft. 428. 7875. 

430. 33.18 lb. I ft. from point of attachment; 18.43 lb., 14.75 lb. 

431. .0504 a;2 Ib.-ft. 432. 289 1b. 434. 808 r. p. m. 
436. 8.12 tons on each. 437. 1665 Ib./sq.-in., 147 mi./hr. 
438. a-3 = 1.38, 0:4 =3.81, IF4 =3.304, an^le between rz and r4= 60° 36.4'. 
443. 9.09 rad/sec 444. 4842 lb. 

445. At P ^ = 24°, at A\ 156° approx., assuming the steam pressure to 
be 16,000 lb. and I large compared to a. 

446. 7.81 rad/sec. (Assumptions as in ans. to 445.) 

447. 9.24 rad/sec. 

448. N' = 9200 lb., iVi =- 58,660 lb., T = - 20,900 lb. 

449. -I- ?!fli 0. • ^50. ^ = for min., TT for max. 

451. For ^ = TT ; .V =- 1000 lb., T= 1000 lb., .Vi =- 92,000 lb. 
For ^ = ; N' =- 1000 lb., P= - 1000 lb., Ni =- 75,650 lb. 

452. P= 250 lb., N' = 4150 lb., A^i =-60,700 lb., T = - 22,300 lb. 

453. N> = 8300 lb., A^i =- 52,300 lb., T = - 16,200 lb., force on crank 
pin = 54,800 lb. 

455. Inversely as the square of the radius of gyration. 

456. 18,900 lb. -ft. 457. 29,250 Ib.-ft. 



ANSWERS 9 

458. [Assume moment of inertia about axis of rotation to be 1660, 
(Prob. 168)] Torque = 2860 Ib.-ft. ; outward. 

459. [Assume moment of inertia of pair of wheels about axis of 
rotation to be 38 (Prob. 170)] Torque = 654 lb. -ft. 

460. 45,700 lb. -ft. 

461. 9.79 r. p. m. ; any real value of w, since A — C. 

462. Precession not steady. 

463. d ranges from 30^^ to 30"^ 29' while Q ranges from to 9.79 r. p. m. 

464. Theoretical lower limit is zero. 475. .47 in., 65,100 lb. /sq. in. 

465. 0, 1370 ft.-lb. 476. .0013 in, 

466. 16.44 f/s, 51.06 ft.-lb. 477. 39,000 Ib./sq. in. 
471. 2611 f/s, 6596 ft.-lb., 30.37 lb. 478. .82 in. 

473. 154.3 tons, 25.7 tons. 479. 932 Ib./sq. in. 

480. 7.54 f/s, 2.81 f/s, 3.16 rad/sec. ; - 4.80 f/s, 4.35 f/s, 4.90 rad/sec. 

481. Point of rod 2.39 ft. from point of impact. Yes. 

484. V= 16.4 f/s, o) = 13.5 rad/sec. 

485. r= 4.26 f/s, w = .884 rad/sec. 486. 9 in. from other end. 

487. .67'7 f/s, .514 rad/sec. ; - 9.95 f/s, .796 rad/sec. 

488. V= 1.08 f/s, w = 2.17 rad/sec. 

489. 16 in. from other end. 491. .704, 41.96 f/s. 

492. V= .621 f/s, w'l = .310 rad/sec, w'2 ^ .207 rad/sec, K. E. lost 
= 1034 ft.-lb. 

493. 2.69 rad/sec, 1.40 rad/sec, 69.5 ft.-lb. 

494. w'l = 1.609 rad/sec, w'g = .7826 rad/sec, K. E. lost = 11,740 
ft.-lb. 



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